You stand in front of a plane mirror whose top is at the same height as the top of your head. Approximately how far down must the mirror extend for you to see your full image? (a) to your chest; (b) to your waist; (c) to your knees; (d) to the floor
The correct answer and explanation is:
The correct answer is (a) to your chest.
To understand this, consider how a plane mirror works. A plane mirror reflects light, so the image formed is a virtual reflection of the actual object, which in this case is your body. The key principle here is that the light from different parts of your body reflects off the mirror and reaches your eyes. In order to see your full image, the mirror only needs to reflect light from the top of your head to your feet.
However, the important point is that you don’t need a mirror that extends the full length of your body to see your full image. The mirror’s height only needs to be half of your actual height. This is because of the way light reflects off the mirror. When light from the top of your head reaches the mirror, it bounces off the mirror at a 45-degree angle and reaches your eyes. Similarly, the light from your feet reaches the mirror and reflects up to your eyes at the same angle. This means that the mirror only needs to reflect the light from the midpoint of your body to give you the full image.
If the top of the mirror is at the same height as the top of your head, it needs to extend down only to about your chest level in order to reflect the light from your feet, providing you with a full view. With this arrangement, the mirror effectively reflects the upper half of your body and the lower half of your body without the need for a full-length mirror.